module BandDiagonalMod #include "shr_assert.h" !----------------------------------------------------------------------- ! !DESCRIPTION: ! Band Diagonal matrix solution ! ! !USES: use shr_log_mod , only : errMsg => shr_log_errMsg use decompMod , only : bounds_type use abortutils , only : endrun use shr_kind_mod , only : r8 => shr_kind_r8 use clm_varctl , only : iulog ! ! !PUBLIC TYPES: implicit none save ! ! !PUBLIC MEMBER FUNCTIONS: public :: BandDiagonal character(len=*), parameter, private :: sourcefile = & __FILE__ !----------------------------------------------------------------------- contains !----------------------------------------------------------------------- subroutine BandDiagonal(bounds, lbj, ubj, jtop, jbot, numf, filter, nband, b, r, u) ! ! !DESCRIPTION: ! Tridiagonal matrix solution ! ! !ARGUMENTS: implicit none type(bounds_type), intent(in) :: bounds integer , intent(in) :: lbj, ubj ! lbinning and ubing level indices integer , intent(in) :: jtop( bounds%begc: ) ! top level for each column [col] integer , intent(in) :: jbot( bounds%begc: ) ! bottom level for each column [col] integer , intent(in) :: numf ! filter dimension integer , intent(in) :: nband ! band width integer , intent(in) :: filter(:) ! filter real(r8), intent(in) :: b( bounds%begc: , 1: , lbj: ) ! compact band matrix [col, nband, j] real(r8), intent(in) :: r( bounds%begc: , lbj: ) ! "r" rhs of linear system [col, j] real(r8), intent(inout) :: u( bounds%begc: , lbj: ) ! solution [col, j] ! ! ! LOCAL VARIABLES: integer :: j,ci,fc,info,m,n !indices integer :: kl,ku !number of sub/super diagonals integer, allocatable :: ipiv(:) !temporary real(r8),allocatable :: ab(:,:),temp(:,:) !compact storage array real(r8),allocatable :: result(:) !----------------------------------------------------------------------- ! Enforce expected array sizes SHR_ASSERT_ALL((ubound(jtop) == (/bounds%endc/)), errMsg(sourcefile, __LINE__)) SHR_ASSERT_ALL((ubound(jbot) == (/bounds%endc/)), errMsg(sourcefile, __LINE__)) SHR_ASSERT_ALL((ubound(b) == (/bounds%endc, nband, ubj/)), errMsg(sourcefile, __LINE__)) SHR_ASSERT_ALL((ubound(r) == (/bounds%endc, ubj/)), errMsg(sourcefile, __LINE__)) SHR_ASSERT_ALL((ubound(u) == (/bounds%endc, ubj/)), errMsg(sourcefile, __LINE__)) !!$ SUBROUTINE SGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO ) !!$* !!$* -- LAPACK driver routine (version 3.1) -- !!$* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. !!$* November 2006 !!$* !!$* .. Scalar Arguments .. !!$ INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS !!$* .. !!$* .. Array Arguments .. !!$ INTEGER IPIV( * ) !!$ REAL AB( LDAB, * ), B( LDB, * ) !!$* .. !!$* !!$* Purpose !!$* ======= !!$* !!$* SGBSV computes the solution to a real system of linear equations !!$* A * X = B, where A is a band matrix of order N with KL subdiagonals !!$* and KU superdiagonals, and X and B are N-by-NRHS matrices. !!$* !!$* The LU decomposition with partial pivoting and row interchanges is !!$* used to factor A as A = L * U, where L is a product of permutation !!$* and unit lower triangular matrices with KL subdiagonals, and U is !!$* upper triangular with KL+KU superdiagonals. The factored form of A !!$* is then used to solve the system of equations A * X = B. !!$* !!$* Arguments !!$* ========= !!$* !!$* N (input) INTEGER !!$* The number of linear equations, i.e., the order of the !!$* matrix A. N >= 0. !!$* !!$* KL (input) INTEGER !!$* The number of subdiagonals within the band of A. KL >= 0. !!$* !!$* KU (input) INTEGER !!$* The number of superdiagonals within the band of A. KU >= 0. !!$* !!$* NRHS (input) INTEGER !!$* The number of right hand sides, i.e., the number of columns !!$* of the matrix B. NRHS >= 0. !!$* !!$* AB (input/output) REAL array, dimension (LDAB,N) !!$* On entry, the matrix A in band storage, in rows KL+1 to !!$* 2*KL+KU+1; rows 1 to KL of the array need not be set. !!$* The j-th column of A is stored in the j-th column of the !!$* array AB as follows: !!$* AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL) !!$* On exit, details of the factorization: U is stored as an !!$* upper triangular band matrix with KL+KU superdiagonals in !!$* rows 1 to KL+KU+1, and the multipliers used during the !!$* factorization are stored in rows KL+KU+2 to 2*KL+KU+1. !!$* See below for further details. !!$* !!$* LDAB (input) INTEGER !!$* The leading dimension of the array AB. LDAB >= 2*KL+KU+1. !!$* !!$* IPIV (output) INTEGER array, dimension (N) !!$* The pivot indices that define the permutation matrix P; !!$* row i of the matrix was interchanged with row IPIV(i). !!$* !!$* B (input/output) REAL array, dimension (LDB,NRHS) !!$* On entry, the N-by-NRHS right hand side matrix B. !!$* On exit, if INFO = 0, the N-by-NRHS solution matrix X. !!$* !!$* LDB (input) INTEGER !!$* The leading dimension of the array B. LDB >= max(1,N). !!$* !!$* INFO (output) INTEGER !!$* = 0: successful exit !!$* < 0: if INFO = -i, the i-th argument had an illegal value !!$* > 0: if INFO = i, U(i,i) is exactly zero. The factorization !!$* has been completed, but the factor U is exactly !!$* singular, and the solution has not been computed. !!$* !!$* Further Details !!$* =============== !!$* !!$* The band storage scheme is illustrated by the following example, when !!$* M = N = 6, KL = 2, KU = 1: !!$* !!$* On entry: On exit: !!$* !!$* * * * + + + * * * u14 u25 u36 !!$* * * + + + + * * u13 u24 u35 u46 !!$* * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 !!$* a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 !!$* a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 * !!$* a31 a42 a53 a64 * * m31 m42 m53 m64 * * !!$* !!$* Array elements marked * are not used by the routine; elements marked !!$* + need not be set on entry, but are required by the routine to store !!$* elements of U because of fill-in resulting from the row interchanges. !Set up input matrix AB !An m-by-n band matrix with kl subdiagonals and ku superdiagonals !may be stored compactly in a two-dimensional array with !kl+ku+1 rows and n columns !AB(KL+KU+1+i-j,j) = A(i,j) do fc = 1,numf ci = filter(fc) kl=(nband-1)/2 ku=kl ! m is the number of rows required for storage space by dgbsv m=2*kl+ku+1 ! n is the number of levels (snow/soil) !scs: replace ubj with jbot n=jbot(ci)-jtop(ci)+1 allocate(ab(m,n)) ab=0.0 ab(kl+ku-1,3:n)=b(ci,1,jtop(ci):jbot(ci)-2) ! 2nd superdiagonal ab(kl+ku+0,2:n)=b(ci,2,jtop(ci):jbot(ci)-1) ! 1st superdiagonal ab(kl+ku+1,1:n)=b(ci,3,jtop(ci):jbot(ci)) ! diagonal ab(kl+ku+2,1:n-1)=b(ci,4,jtop(ci)+1:jbot(ci)) ! 1st subdiagonal ab(kl+ku+3,1:n-2)=b(ci,5,jtop(ci)+2:jbot(ci)) ! 2nd subdiagonal allocate(temp(m,n)) temp=ab allocate(ipiv(n)) allocate(result(n)) ! on input result is rhs, on output result is solution vector result(:)=r(ci,jtop(ci):jbot(ci)) ! DGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO ) call dgbsv( n, kl, ku, 1, ab, m, ipiv, result, n, info ) u(ci,jtop(ci):jbot(ci))=result(:) if(info /= 0) then write(iulog,*)'index: ', ci write(iulog,*)'n,kl,ku,m ',n,kl,ku,m write(iulog,*)'dgbsv info: ',ci,info write(iulog,*) '' write(iulog,*) 'ab matrix' do j=1,n ! write(iulog,'(i2,7f18.7)') j,temp(:,j) write(iulog,'(i2,5f18.7)') j,temp(3:7,j) enddo write(iulog,*) '' call endrun( 'BandDiagonal ERROR: dgbsv returned error code' ) endif deallocate(temp) deallocate(ab) deallocate(ipiv) deallocate(result) end do end subroutine BandDiagonal end module BandDiagonalMod